362
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.102 The thermal resistance of the contact point under different conductivity ratios
k c = ε r k f + k area + k point = N (1 − ε r )
1
π d R
point
+ k s η
+ ε r k f .
(5.232)
It can be found that the conductive effective thermal conductivity is affected by the
average coordination number, the void fraction, the contact radius, and the thermal
conductivities of fluid and particle. The parameter analysis will be discussed in the
following section.
5.5.2.2 Validation in Vaccum Without Interstitial Fluids
For the particle system under vacuum condition between particles, there is no (PFP)
contribution of conduction through fluids to the effective thermal conductivity, and
2k s r c
k f d
1 is always satisfied for computing the area contact resistance (PPA).
Sakatani et al. [143] performed the experiment of powder materials to measure the
effective thermal conductivity of different void fractions in vacuum condition [143].
The glass spheres are 5 µm in diameter. Equation (5.225) is applied to calculating
k area , and the coordination number of the powdered materials suggested by [143] is
written as
N =
2.812(1 − ε r ) (−
1
3 )
f 2 (1 + f 2 )
(5.233)
where f = 0.07318 + 2.193ε r − 3.357ε
2
r + 3.194ε
3
r (Fig. 5.103).
5 Numerical Models for Pebble-Bed Heat Transfer
Fig. 5.102 The thermal resistance of the contact point under different conductivity ratios
k c = ε r k f + k area + k point = N (1 − ε r )
1
π d R
point
+ k s η
+ ε r k f .
(5.232)
It can be found that the conductive effective thermal conductivity is affected by the
average coordination number, the void fraction, the contact radius, and the thermal
conductivities of fluid and particle. The parameter analysis will be discussed in the
following section.
5.5.2.2 Validation in Vaccum Without Interstitial Fluids
For the particle system under vacuum condition between particles, there is no (PFP)
contribution of conduction through fluids to the effective thermal conductivity, and
2k s r c
k f d
1 is always satisfied for computing the area contact resistance (PPA).
Sakatani et al. [143] performed the experiment of powder materials to measure the
effective thermal conductivity of different void fractions in vacuum condition [143].
The glass spheres are 5 µm in diameter. Equation (5.225) is applied to calculating
k area , and the coordination number of the powdered materials suggested by [143] is
written as
N =
2.812(1 − ε r ) (−
1
3 )
f 2 (1 + f 2 )
(5.233)
where f = 0.07318 + 2.193ε r − 3.357ε
2
r + 3.194ε
3
r (Fig. 5.103).